s1248 — the chiral anchor on F0: C56 and the parity; θ in-house; the D56 line on the circle through o; T3a
receipts {'s1239': '5a5c62f3770072d8'}
  symmetries  {'C56_commutes_with_parity': True, 'C56_commutes_with_D56': True, 'CP_is_an_antisymplectic_involution_fixing_X': True, 'J0_moves_X': 1.414214}
  frame       {'canonical': True, 'X_vanishes_on_the_magnetic_span': True, 'rank_of_X_on_the_electric_span': 28, 'parity_is_plus_one_on_electric_minus_one_on_magnetic': True, 'C56_on_the_massless_electric_directions': [-1.0, -1.0, -1.0, -1.0], 'J0_maps_v_i_to_minus_f_i': True, 'O_on_y': [1.0, 1.0, 1.0, -1.0, -1.0, -1.0], 'J0_on_y': [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0], 'C56_on_y': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0]}
  theta       {'equals_the_lanes_printed_formula_at_20_points': True, 'K_equals_G_inverse': True, 'control_transposed_product_min_deviation': 0.1255, 'parity_odd': True, 'C_even': True, 'zero_on_the_a_flat': True}
  D56_line    {'+0.5': {'theta_eigen_triplet': 0.117308537, 'theta_eigen_singlet': -0.339523099, 'K_eigen_triplet': 0.993095518, 'K_eigen_singlet': 0.940597717}, '+1.0': {'theta_eigen_triplet': 0.231432267, 'theta_eigen_singlet': -0.608859365, 'K_eigen_triplet': 0.972851019, 'K_eigen_singlet': 0.793278182}, '-2.0': {'theta_eigen_triplet': -0.439333443, 'theta_eigen_singlet': 0.888385562, 'K_eigen_triplet': 0.898324065, 'K_eigen_singlet': 0.459098131}, '+3.0': {'theta_eigen_triplet': 0.608859365, 'theta_eigen_singlet': -0.971667928, 'K_eigen_triplet': 0.793278182, 'K_eigen_singlet': 0.236350243}}
  u0_slice    {'theta2_plus_K2_is_one_at_10_points': True, 'control_generic_min_deviation': 0.3213}
  T3a         {'D56_levels_and_multiplicities': {'-6': 1, '-2': 27, '+2': 27, '+6': 1}, 'eps_signs_over_12_seeded_E': [1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1], 'C56_keeps_eps': True, 'unbroken_algebra_at_the_line_point_dim': 16, 'O_flips_eps_and_the_end': True, 'S_flips_eps_at_fixed_end_but_maps_X_to_X_minus_omega': True}
  receipt   PASS s1239_is_the_filed_kernel_whose_head_supplies_the_substrate
  receipt   PASS s1241_is_the_filed_kernel_whose_coupling_reading_and_massless_directions_are_copied
  receipt   PASS s1232_is_the_filed_kernel_whose_parity_and_X_pieces_are_copied
  receipt   PASS s1243_is_the_filed_house_check_of_C56
  receipt   PASS s1226_is_the_filed_kernel_where_eps_is_the_sign_of_the_cubic_norm
  receipt   PASS the_filed_lane_report_whose_printed_theta_formula_is_graded
  computed  PASS the_lanes_printed_formula_is_the_object_graded
  receipt   PASS s1225_is_the_filed_evaluator_kernel_executed_head_only
  receipt   PASS s1235_is_the_filed_kernel_whose_charge_construction_is_copied
  receipt   PASS s1238_is_the_filed_house_check_of_the_lanes_point_c_c
  receipt   PASS the_filed_A1764_lane_report_is_the_source_of_B_c_and_of_the_lattice_weights_NOT_imported
  receipt   PASS s1220_is_the_filed_kernel_whose_construction_is_copied
  receipt   PASS s121a_is_the_file_whose_potential_is_copied
  computed  PASS the_two_generator_stacks_agree
  computed  PASS golden_vacuum_is_a_Minkowski_critical_point_as_s121a_says
  computed  PASS golden_vacuum_is_2lnphi_from_the_origin
  receipt   PASS s640_lib_is_the_S220_A_layer_executed_verbatim
  receipt   PASS s646_is_the_source_of_the_SV_vector_operator_executed_verbatim
  receipt   PASS s645c_results_hold_the_P6_gradient_reproduced_here
  computed  PASS the_S220_frame_is_this_kernels_frame
  computed  PASS Z0_the_torus_T0_its_fixed_directions_p0_and_three_commuting_sl2R_planes
  computed  PASS W1_C56_commutes_with_the_parity_and_with_D56_and_CP_is_an_antisymplectic_symmetry_of_X_that_reverses_charges_and_the_line
  computed  PASS W2_the_frame_is_fixed_by_the_gauging_and_the_parity_and_C56_is_minus_one_on_the_massless_vectors
  computed  PASS W3_the_theta_matrix_derived_in_house_from_the_coset_representative_equals_the_lanes_printed_closed_form
  computed  PASS W4_theta_is_parity_odd_C_even_hence_CP_odd_zero_on_the_a_flat_and_nonzero_off_it
  computed  PASS W5_on_the_D56_line_theta_and_K_have_closed_forms_with_common_eigenvectors_and_every_eigen_coupling_has_modulus_one
  symbolic  PASS W5s_lane_formula_on_the_line_diagonal
  symbolic  PASS W5s_lane_formula_on_the_line_offdiagonal
  symbolic  PASS W5s_singlet_theta_eigenvalue_is_minus_tanh_3x
  symbolic  PASS W5s_singlet_G_eigenvalue_is_cosh_3x
  symbolic  PASS W5s_triplet_G_eigenvalue_is_cosh_x
  computed  PASS W6_on_the_u0_slice_theta_squared_plus_K_squared_is_one_and_theta_commutes_with_K
  computed  PASS W7_T3a_eps_takes_both_signs_at_each_end_C56_and_the_unbroken_group_keep_it_the_parity_flips_it_with_the_end
  computed  PASS W7c_CONTROL_the_end_preserving_eps_flip_S_exists_in_the_normaliser_but_is_not_a_symmetry_of_the_gauging
  argument  ARG  u0_identity_from_the_two_covariances
  argument  ARG  what_board_T4_now_reads
  argument  ARG  T3a_outcome
  argument  ARG  the_mirror_as_electric_magnetic_duality
  argument  ARG  limits

VERDICT C56 commutes with the parity O and with D56; CP = C56·O is an anti-symplectic symmetry of X reversing the charges and the line. The θ-matrix of the four massless vectors, derived in-house in the frame fixed by the gauging and the parity, equals the lane's printed −HG⁻¹ (20 points); it is P-odd, C-even, CP-odd, zero on the a-flat. On the D56 line θ has eigenvalues tanh(s/(3√2)) ×3 and −tanh(s/√2), K has sech of the same, and every eigen-coupling has |τ| = 1; on the whole u = 0 slice θ² + K² = 1. T3a: ε takes both signs at each end; symmetries keeping the end keep ε; the parity flips both — one bit only up to a convention no registered object fixes.
RESULT_HASH 6ab7f4efe3faffb4
s1248: 14 computed, 5 symbolic, 15 receipt, 5 argument, 0 failed
